Obtain the echlone form hence solve the equations x+2y+3z=-1 2x-y-2z=3 z+2y+2x=2?

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Answer 1 · 2017-09-23T09:06:21

The solution is #((x),(y),(z))=((7/9),(7/9),(-10/9))#

The augmented matrix is

#( (1,2,3,|,-1), (2,-1,-2,|,3), (2,2,1,|,2) )#

Perform the following operations on the rows

#R2larrR2-2R1# and #R3larrR3-2R1#

#( (1,2,3,|,-1), (0,-5,-8,|,5), (0,-2,-5,|,4) )#

#R2larr(R2)/(-5)# and #R3larr(R3)/(-2)#

#( (1,2,3,|,-1), (0,1,8/5,|,-1), (0,1,5/2,|,-2) )#

#R1larrR1-2R2# and #R3larrR3-R2#

#( (1,0,-1/5,|,1), (0,1,8/5,|,-1), (0,0,9/10,|,-1) )#

#R3larrR3*10/9#

#( (1,0,-1/5,|,1), (0,1,8/5,|,-1), (0,0,1,|,-10/9) )#

#R2larrR2-8/5R3#

#( (1,0,-1/5,|,1), (0,1,0,|,7/9), (0,0,1,|,-10/9) )#

#R1larrR1+1/5R3#

#( (1,0,0,|,7/9), (0,1,0,|,7/9), (0,0,1,|,-10/9) )#